Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 20 / c / Solution

The curl gives the vorticity:Since $x\mathbf{i}+y\mathbf{j}=\rho \hat{\mathbf{\rho }}$, the requested form isAt the axis the radial unit vector is undefined, but its coefficient vanishes and the Cartesian expression remains smooth. The radial vorticity reflects the change in rotation rate with height.